Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
int mn=100001,n,i,j,a[1000],k,x,y,mx=0;
double sum=0.0,tes;
int main(void)
{
	cin>>n;
	for(i=0;i<n;i++) cin>>a[i];
	sort(a,a+n);
	for(i=0;i<n-1;i++){
		for(j=i+1;j<n;j++){
			if(a[j]-a[i]<mn) mn=a[j]-a[i],y=j;
		}
		//cout<<"mn"<<" "<<y<<endl;
		for(j=n-1;j>=0;j--){
			if(j!=i&&j!=y){
				for(k=j-1;k>=0;k--){
					if(k!=y&&k!=i){
						tes=(double)(a[j]+a[k])/mn;
						if(sum<tes){
							sum=tes;
							break;
						}
					}
				}
				//cout<<j<<" "<<sum<<endl;;
				break;
			}
		}
	}
	printf("%.6f\n",sum);
	return 0;
}